In many applications for chemometrics etc., indirect measurements and direct measurements (e.g. concentrations) of samples are used to develop a calibration curve, which can be used to predict a direct measurement from an indirect measurement. In some cases, Y can be one or more indirect measurements (e.g., multivariate data) and X can be the direct measurement. A calibration curve can be developed between X and Y, and normality assumptions made for the distributions of X and Y.
In many instances, the direct variable X is continuous, and residual analysis can be used to determine the calibration curve. Such predictions are not applicable to the situation where X is a class variable, i.e. X corresponds to two (binary) or more classes. In many applications, the direct measurements could be a class variable; and in this case, logistic regression or discriminant analysis can be used for predicting the class based upon the indirect measurement and the relationship between indirect measurements and direct measurements.
In logistic regression, the classification is assigned on the basis of likelihood/probability of being in each class. The normality assumption is made for the indirect measurements, and classification is achieved in terms of odds ratio computation.
In discriminant analysis, a linear distance of indirect measurements from different classes is calculated, and the class is assigned on the basis of a minimum distance. In this case too, a normality assumption is made for the distribution of indirect measurements. In certain applications, it is of interest to discriminate classes near a cutoff from one class to another, e.g., in the determination of the presence or absence of an analyte in a sample.
But, such a discrimination can be difficult to perform accurately, thereby diminishing the sensitivity and specificity. Such a discrimination can be even more difficult to determine accurately when there are multiple indirect measurements over time, as can happen in flash reactions (e.g., involving methicillin-resistant Staphylococcus aureus, MRSA).